COVID-19 case doubling time associated with non-pharmaceutical interventions and vaccination: A global experience

Background Evidence has revealed that nonpharmaceutical interventions (NPIs) were effective in attenuating the spread of COVID-19. However, policymakers have encountered difficulty in identifying the most effective policies under different circumstances. This study investigated the relative effectiveness of different NPIs and vaccination in prolonging COVID-19 case doubling time (DT). Methods The study sample consisted of observations from 137 countries during 1 January 2020 to 13 June 2021. DT was calculated on a daily basis per country. Data were retrieved from the Oxford COVID-19 Government Response Tracker, World Development Indicators, and Worldwide Governance Indicators. To capture policy intervention dynamics, we combined a random-effect growth-curve model with nonstandard interrupted time series analysis. We also evaluated the association of policy measures with DT for different outbreak stages and levels of government effectiveness. Results Vaccine rollouts, workplace closures, and school closures were relatively effective. For each day that these measures were implemented, the DT increased by 1.96% (95% confidence interval (CI) = 0.63 to 3.29; P = 0.004), 1.41% (95% CI = 0.88 to 1.95%; P < 0.001) and 1.38% (95% CI = 0.95 to 1.81%; P < 0.001), respectively. Workplace and school closures were positively associated with DT at all stages; however, the associations weakened in later stages, where vaccine rollouts appeared to be most effective in prolonging DT (95% CI = 1.51% to 3.04%; P < 0.05). For countries with a high level of government effectiveness, most of the containment measures evaluated were effective; vaccine rollouts had the greatest effect size. For countries with medium or low levels of government effectiveness, only the closure of workplaces was consistently associated with prolonged DT. Conclusions The effectiveness of vaccine rollouts outweighed that of NPIs, especially in the later outbreak stages. However, vaccination was not associated with prolonged case DT in countries with lower levels of government effectiveness, probably due to low vaccine coverage. Among the NPIs examined, workplace closures were highly effective across all outbreak stages and levels of government effectiveness. Our findings suggest that mass vaccination is critical to reducing SARS-CoV-2 transmission, especially in countries where NPIs are less effective.

Appendix S1 Flow chart of the study sample Merged with Worldwide Governance Indicators (WGI) data. Faeroe Islands was removed due to not in the WGI database. 42 countries/regions were removed due to the following exclusion criterion: (a) fewer than 500 confirmed cases as of 13 June 2021; (b) missing data in the OxCGRT database for more than 90 days; (c) fewer than 1 million populations, and (d) fewer than 40 observations for the case doubling time variable.

Appendix S2 Sample countries, observed country days and government effectiveness scores
The study sample is composed of 137 countries over the period of 1st January 2020 -13rd June, 2021. Observed country days refers to days since the first reported COVID-19 case until the last day after which the case doubling time (the outcome variable) could not be calculated. See Methods for calculation of case doubling time. The government effectiveness scores range from -2.5 to 2.5, with a higher value indicating higher government effectiveness. We applied the latest 2019 scores. For subgroup analysis presented in Figure 3 in the main text, we ranked countries according to their effectiveness scores and divided them into three equal-sized groups: low, medium and high, denoted by L, M, and H, respectively in Table S2.  Table S3 provides the definition of policy measures used in this study and the corresponding OxCGRT indicators. We focused on interventions that were actually enforced; thus for most OxCGRT indicators, degree of 0 and 1 were treated as the reference group, i.e. no measures. In addition, we combined the highest two degrees for stay-at-home requirements, testing policies, and face covering. For vaccine rollout, we combined degrees of 1−5 into a single category because the number of country-days for individual degrees was relatively small.  Table S4 were calculated based on 137 sample countries over the period of 1 st January 2020 -13 rd June, 2021. The most frequently adopted policy was "workplace closures for some sectors or categories" (355 times), followed by "requirements to stay-at-home with exceptions for daily exercise, grocery shopping and essential trips" (289 times), and school closures at all levels (272 times). With respect to average duration, coordinated public information campaigns had the longest days (358 days), followed by comprehensive contact tracing (218 days) and cancellation of public events (168 days).   (1) in the main text. The mean log of case doubling time was 3.8. The mean number of weeks from the first reported death to the earliest intervention was −7.26, indicating that countries generally adopted at least one policy measure before the first death was reported. year, we replaced that missing value with the country's recoded value from the previous one or two years. Figure S6 illustrates the number of countries out of 137 sample countries that adopted respective policy measures each day from 1 January 2020 to May 31 2021. The X-axis denotes calendar date. For example, Jan20 refers to January 2020, and May21 refers to May 2021. Data for all policy measures were obtained from Oxford COVID-19 Government Response Tracker (OxCGRT) indicators database. Figure S6. Number of countries implemented the 11 policy measures by calendar date. Note: UHC=universal health coverage; GDP=gross domestic product. Note: All models included the time trend, quadratic terms of time and policy variables, and country-specific random intercepts and random coefficients of time. Country-clustered robust standard errors were used. Legend: * p<0.05; ** p<0.01; *** p<0.001. Note: UHC=universal health coverage; GDP=gross domestic product. PPP=purchasing power parity. Note: All models included the time trend, quadratic terms of time and policy variables, and country-specific random intercepts and random coefficients of time.

Appendix S8 Sensitivity analysis: results from alternative specifications
Sensitivity analysis was conducted to check the robustness of the study results. We examined the collinearity by calculating the correlation coefficient (cc) of each pair of policy variables, and excluded those that had a cc greater than 0.4. As Table S8.1 shows (figures in bold), cancellation of public events (ID=5) was highly correlated with full school closures (0.42), partial workplace closures (0.41) and restriction on gatherings to 10 people (0.44). Coordinated public campaigns (ID=11) was highly correlated with widespread testing (0.46), comprehensive contact tracing (0.49), and face covering required in all places (0.46). Therefore, we excluded these two policy measures one by one from the main model. The results are presented under the heading of Model S1 and Model S2 in Table S8.2. We found that results from alternative specifications are generally consistent with those from the main model, except that in Model S1 "Restriction on gatherings to 10 people" became positively associated with prolonged case doubling time.

Appendix S9 Residual diagnostics
a. Distribution of predicted random intercepts for 137 countries b. Distribution of predicted random slopes for 137 countries Figure S9. Residual diagnostics. This study used the empirical Bayes prediction method to assign values to country-specific random intercepts and random slopes, and assumed that they have a normal distribution. a.
Distribution of predicted random intercepts for 137 countries. b. Distribution of predicted random slopes for 137 countries. Predicted random slopes are positively skewed, but in general predicted random effects are close to normal distributions.

Appendix S10 Cross validation of the study results
To check the stability and robustness of the study results, a cross-validation method was applied. First, we randomly assigned 50% of the data for individual countries as the training data, and saved the remaining data for testing (validation). Second, we ran the regression (Equation (1) in the main text) using the training data to obtain coefficient estimates and country-specific random intercepts and slopes of time. Third, we predicted the case doubling time (DT) for the testing data using the estimated model and compared the fitted with observed DT (Table S10.1). The equation for prediction is given by Equation (S1) in Appendix S11. Finally, the DT regression was run on the testing data; the results were compared with those from the training data and from the full sample (Table S10.2). We also performed random forest algorithm using Stata command rforest and compared the prediction accuracy with that of the random-effect growth-curve model. The RMSE converged prior to100 iterations; thus we set iterations to be 100. The lowest validation RMSE (calculated against the testing data) occurred at 0.22 when the number of randomly selected variables at each split was 7.
This result shows that random forest model had a slightly higher prediction accuracy than the empirical model used in this study. For the present study, the goal was to estimate the relative effectiveness of a wide range of policy measures (which increased the RMSE); hence the random forest model was used for validation only. Note: All models included the time trend, quadratic terms of time and policy variables, and country-specific random intercepts and random coefficients of time. Country-clustered robust standard errors were used. Legend: * p<0.05; ** p<0.01; *** p<0.001. Figure S11 Predicted versus observed trends of case doubling time for 137 countries